Past exam of the mathematical methods I course of the University of Oxford / 2015 / 7 / Solution

Subtract the first vertex from the remaining three to obtain edge vectors $a=(1,2,-2)$, $b=(0,1,3)$, $c=(-1,-1,0)$. Their scalar triple product isA tetrahedron occupies one sixth of the corresponding parallelepiped, so its volume isThe absolute value removes the orientation sign of the determinant.